Hi, there--

THE PROBLEM:
The graph of f(x)=x^2 will be translated 5 units up and 2 units to the right.  What is the 
function that describes the graph produced by the translation?

A SOLUTION:
A vertical translation (a shift) has the form g(x) = f(x) + c where g(x) is the transformed  
function and c is the number of units. If c>0, the function shits up. If c<0, the shift is down.

A horizontal translation has the form g(x) = f(x+c) where g(x) is the c s the number of units 
shift left or right. If c>0 the function shifts left. If c<0 the function shifts right.

Putting this all together we shift 5 units up.
g(x) = x^2 + 5

Then we shift 2 units to the right.
g(x) = (x-2)^2 + 5

Hope that helps!
Mrs. Figgy
math.in.the.vortex@gmail.com